If function  f   and  g given by f(x) =log⁡(x−1)−log⁡(x−2) and g(x)=log⁡x−1x−2  are equal then x lies in the interval

f(x)  is defined for all x satisfying x−1>0  and  x−2>0 i.e. x>2 Domain (f)=(2,∞)                       .......              (i)gx  is defined for all x satisfyingx−1x−2>0⇒x∈(−∞,1)∪(2,∞)Domain (g)=(−∞,1)∪(2,∞)      ……….(ii) Thus f(x)  and  g(x) are equal for all x belonging to theircommon domain i.e  (2,∞)